Plot y =
The roots of the polynomial are:
x1 = 1
x2 = 1
x3 = 1
x4 = 1
x5 = 1
x6 = −1
x7 =
x8 = -Explanation
This is a polynomial of degree 8. To find zeros for polynomials of degree 3 or higher we use Rational Root Test.
The Rational Root Theorem tells you that if the polynomial has a rational zero then it must be a fraction p/q,
where p is a factor of the trailing constant and q is a factor of the leading coefficient.
The factor of the leading coefficient (1) is 1 .The factors of the constant term (2) are 1 and 2.
Then the Rational Roots Tests yields the following possible solutions:
±11, ±21.
Substitute the POSSIBLE roots one by one into the polynomial to find the actual roots. Start first with the whole numbers.
If we plug these values into the polynomial P(x), we obtain P(1)=0.
To find remaining zeros we use Factor Theorem. This theorem states that if pq is root of the polynomial
then this polynomial can be divided with qx−p. In this example:
Divide P(x) with x−1
=
Polynomial can be used to find the remaining roots.
Use the same procedure to find roots of x^7−3x^6+8x^4−7x^3−3x^2+6x−2.
When you get second degree polynomial, you will easily find two remaining roots.
